This study aims to articulate and compare the structure, presuppositions and implications of two paradigmatic sceptical arguments, i.e. arguments from underdetermination of scientific theories by observational data (UA) and Cartesian-style arguments (CA) invoking sceptical scenarios of severe cognitive dislocation. Although salient analogies between them may prompt one to think that a unified diagnosis of what is amiss with them is called for, it will be argued that this may be a false hope, if those analogies do not underwrite a complete homology. That said, possible parallels of one promising anti-sceptical exposure of CA are pointed out for the case of UA, which conspire together to render the problem of underdetermination less threatening than it could at first appear.